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Ab initio recombination in the expanding ultracold plasmas

Yurii V. Dumin, Ludmila M. Svirskaya

Abstract

The efficiency of recombination is of crucial importance for the existence of ultracold plasmas, particularly, the ones formed in the magneto-optical traps. Unfortunately, a straightforward simulation of the recombination encounters the problem of huge difference in the spatial and temporal scales for free and bound motion of the electrons. As a result, only the "virtual" electron-ion pairs are usually reproduced in such simulations, and it is necessary to employ some additional criteria to identify them with the recombined atoms (this might be a minimal number of revolutions of the electron about the nearest ion or a maximal distance between them). It is the aim of this paper to present the first successful ab initio simulation of the recombination without any auxiliary assumptions. We employed a special algorithm, which was based on: (i) using the "scalable" reference frame, co-moving with the expanding plasma, (ii) dynamical choice of the number of "mirror" cells, taking into account in calculation of the Coulomb sums, and (iii) accurate treatment of the singular interparticle interactions, without any truncation or "softening" of the Coulomb forces. Then, the recombination events are identified by a series of sharp equidistant peaks in the kinetic and/or potential energies for a sample of particles, which are caused by the captured electrons passing near the pericenters of their orbits; and this is confirmed by a detailed inspection of the particle trajectories. Thereby, we were able to trace formation of the real - rather than "virtual" - electron-ion pairs. The total efficiency of recombination for the realistic experimental conditions was found to be about 20%, which is in perfect agreement both with the laboratory measurements and with the earlier semi-empirical simulations.

Ab initio recombination in the expanding ultracold plasmas

Abstract

The efficiency of recombination is of crucial importance for the existence of ultracold plasmas, particularly, the ones formed in the magneto-optical traps. Unfortunately, a straightforward simulation of the recombination encounters the problem of huge difference in the spatial and temporal scales for free and bound motion of the electrons. As a result, only the "virtual" electron-ion pairs are usually reproduced in such simulations, and it is necessary to employ some additional criteria to identify them with the recombined atoms (this might be a minimal number of revolutions of the electron about the nearest ion or a maximal distance between them). It is the aim of this paper to present the first successful ab initio simulation of the recombination without any auxiliary assumptions. We employed a special algorithm, which was based on: (i) using the "scalable" reference frame, co-moving with the expanding plasma, (ii) dynamical choice of the number of "mirror" cells, taking into account in calculation of the Coulomb sums, and (iii) accurate treatment of the singular interparticle interactions, without any truncation or "softening" of the Coulomb forces. Then, the recombination events are identified by a series of sharp equidistant peaks in the kinetic and/or potential energies for a sample of particles, which are caused by the captured electrons passing near the pericenters of their orbits; and this is confirmed by a detailed inspection of the particle trajectories. Thereby, we were able to trace formation of the real - rather than "virtual" - electron-ion pairs. The total efficiency of recombination for the realistic experimental conditions was found to be about 20%, which is in perfect agreement both with the laboratory measurements and with the earlier semi-empirical simulations.
Paper Structure (9 sections, 12 equations, 5 figures)

This paper contains 9 sections, 12 equations, 5 figures.

Table of Contents

  1. Introduction
  2. The algorithm of simulation
  3. Geometrical configuration
  4. The scalable reference frame
  5. The method of integration
  6. Initial conditions
  7. Results of the Simulations
  8. Discussion
  9. Conclusions

Figures (5)

  • Figure 1: Sketch of calculation of the Coulomb sums, where each electron $e$ interacts not only with a specified ion $i$ in the basic cell (solid arrow) but also with infinite number of its mirror images $i^\prime$ (dashed arrows).
  • Figure 2: Sketch of summation over the mirror cells (dotted squares) around the basic cell (solid square) in calculation of the Coulomb forces.
  • Figure 3: Temporal dependence of the kinetic (red curves) and potential (blue curves) energies of all particles in the basic cell at various "magnifications" (successive panels, from top to bottom). The regions of subsequent magnification are marked by the rectangles.
  • Figure 4: Trajectory of the first (short-period) captured electron viewed in three coordinate planes at two different magnifications (three top and three bottom panels, respectively). The region of formation of a captured state of the electron is marked by the red dotted circle. The coordinate scales in various directions are different.
  • Figure 5: Trajectory of the second (long-period) captured electron viewed in three coordinate planes. The region of formation of a captured state of the electron is marked by the red dotted circle. The coordinate scales in various directions are different.